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ihermite

  

integer-only Hermite Normal Form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ihermite(A)

ihermite(A, U)

Parameters

A

-

rectangular matrix of integers

U

-

name

Description

• 

Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[HermiteForm], instead.

  

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

• 

The function ihermite computes the Hermite Normal Form (reduced row echelon form) of a rectangular matrix of integers.

• 

The Hermite normal form of A is an upper triangular matrix H with rank(A) = the number of nonzero rows of H.  If A is an n by n matrix of full rank then i],i=1..nH[i.

• 

This is not an efficient method for computing the rank or determinant except that this may yield a partial factorization of detA without doing any explicit factorizations.

• 

The Hermite normal form is obtained by doing elementary row operations. This includes interchanging rows, multiplying through a row by -1, and adding an integral multiple of one row to another.

• 

One can use transposes to obtain column form of the Hermite Normal Form.

• 

In the case of two arguments, the second argument U will be assigned the transformation matrix on output, such that the following holds: ihermite(A) = U A.

• 

The command with(linalg,ihermite) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

withlinalg:

Harray9,36,30,36,192,180,30,180,180

H9−3630−36192−18030−180180

(1)

ihermiteH

303001200060

(2)

To obtain column form of Hermite Normal Form

transposeihermitetransposeH

300012030060

(3)

Aarray3,7,11,13,17,19:

BihermiteA,U

B1296104086

(4)

evalU

9−213−3

(5)

evalmU &* AB

000000

(6)

See Also

linalg(deprecated)[det]

linalg(deprecated)[hermite]

linalg(deprecated)[ismith]

linalg(deprecated)[rank]

LinearAlgebra

LinearAlgebra[HermiteForm]